3 * Copyright (C) 2004 Free Software Foundation, Inc.
4 * Written by Jason H. Stover.
6 * This program is free software; you can redistribute it and/or modify
7 * it under the terms of the GNU General Public License as published by
8 * the Free Software Foundation; either version 2 of the License, or (at
9 * your option) any later version.
11 * This program is distributed in the hope that it will be useful, but
12 * WITHOUT ANY WARRANTY; without even the implied warranty of
13 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
14 * General Public License for more details.
16 * You should have received a copy of the GNU General Public License
17 * along with this program; if not, write to the Free Software
18 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
21 * Computes the cumulative distribution function for a Poisson
22 * random variable. For a Poisson random variable X with parameter
25 * Pr( X <= k ) = Pr( Y >= p )
27 * where Y is a gamma random variable with parameters k+1 and 1.
31 * W. Feller, "An Introduction to Probability and Its
32 * Applications," volume 1. Wiley, 1968. Exercise 46, page 173,
36 #include <gsl/gsl_math.h>
37 #include <gsl/gsl_errno.h>
38 #include <gsl/gsl_cdf.h>
39 #include "gsl-extras.h"
42 * Pr (X <= k) for a Poisson random variable X.
45 gslextras_cdf_poisson_P (const long k, const double lambda)
52 GSLEXTRAS_CDF_ERROR ("lambda <= 0", GSL_EDOM);
61 P = gsl_cdf_gamma_Q ( lambda, a, 1.0);
67 * Pr ( X > k ) for a Possion random variable X.
70 gslextras_cdf_poisson_Q (const long k, const double lambda)
77 GSLEXTRAS_CDF_ERROR ("lambda <= 0", GSL_EDOM);
86 P = gsl_cdf_gamma_P ( lambda, a, 1.0);